Constraints and Inverse - Needs Some Explaining
If you use set inverse:


the object get parented as it is
the child won't be affected by the initial transformation of the parent


If you use clear inverse:


the parent transformations get cleared (momentarily)
the object get parented 
the transformation of the parent get is restored (as if you have parented then transformed the parent which will effect the child)


all this is just setting the matrix that relates the child to the world space

To keep the object transformation inherited from the parent, apply the visual transformation and set the influence to 0 (or remove the constraint).



Example: two cubes one at the center (will be used as parent) 
initial state: (no constraints yet ) 



the parent transformed: (no constraints yet) the cube moved scaled and rotated


after this we add the child of constraint to the smaller cube

child of constraint with set inverse: child is not affected by the parent initial transformation



child of constraint with clear inverse: child is affected by the parent initial transformation